Total irregularity strength of m-copies of rhombus graph

Abstract

Let G = (V, E) is a graph. Total k-labeling on G is a mapping from V ∪ E to {1,2,3,…,k}. The weight of the vertex v ∈ V is the sum of the label of v and the labels of all the edges incident with v. While the weight of the edge uv ∈ E is the sum of the label of uv and the label of u and v. A total k-labeling of G is called a totally irregular total labeling, if the weight of every two distinct vertices are different and the weight of every two distinct edges are different. The minimum k such that a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G). In this paper, we obtain ts of m-copies of rhombus graph